Math
1,470 math calculators: percentages, fractions, equations, geometry, trigonometry, statistics and number theory. Each one shows the method in plain words, so you get the answer and understand how it was reached, free in your browser.
Continuous uniform CDF calculator
For a uniform distribution from 2 to 10, the chance of a value at or below 5 is 0.375. Enter the two bounds and a point: values below the range give zero…
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Negative Binomial Mean and Variance Calculator
With a target of 5 successes and a 0.4 chance of success on each trial, you can expect 7.5 failures on average before the fifth success.
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Normal distribution CDF calculator
If x equals the mean, such as 0 on the standard normal curve, the cumulative probability is 0.5: half the curve lies to its left.
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Z-score from normal value calculator
A score of 85 on a test with mean 70 and standard deviation 10 has a z-score of 1.5: one and a half standard deviations above the mean.
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Percentile to z-score calculator
The 95th percentile matches a z-score of 1.64485362513 on the standard normal curve. Enter any percentile between 0 and 100, decimals included, and get the…
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Confidence Interval for Variance Calculator
A sample variance of 4 from 25 observations gives a 95 percent interval for the population variance that reaches further above 4 than below it, because the…
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Exponential mean and variance calculator
At a rate of 2 events per hour, the average wait is 0.5 hours, the variance 0.25 and the standard deviation 0.5.
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F Critical Value Calculator
With 5 and 10 degrees of freedom and a 0.05 level, you get the F value that leaves 5 % of the distribution in the upper tail.
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Gamma distribution PDF calculator
Get the gamma probability density at any point from a positive shape and rate, plus its natural logarithm for very small values; a shape of 1 turns it into the…
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Probability distribution validity checker
Four masses of 0.25 each pass the check with a sum of exactly 1. Paste a list of probabilities and see at once whether it is a valid distribution, which entries…
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Standard normal probability calculator
The area between z values of −1.96 and 1.96 is about 95 % of the standard normal curve. Enter a lower and an upper z to get the probability between them, the…
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Student t Distribution CDF Calculator
At t of 1.5 with 10 degrees of freedom, a little over nine tenths of the Student t distribution lies at or below that value.
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Confidence interval for paired differences
Six before-and-after pairs with differences of 2, 4, −2, 4, 5 and 3 give a 95 percent interval for the average change that sits entirely above zero.
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Clopper-Pearson Exact Confidence Interval Calculator
Seven successes out of 10 give an estimate of 0.7 and an exact 95 percent interval stretching from just over a third to above nine tenths.
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Confidence Level and Alpha Calculator
A 95 percent confidence level, entered as 0.95, leaves an alpha of 0.05, split into 0.025 in each tail.
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P-value from z-score calculator
A z of 1.96 in a two-sided test gives a p-value of almost exactly 5%. Choose the left, right or two-sided tail to match your question, and the probability comes…
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Sample Size for a Proportion Calculator
To estimate a share within 5 percentage points at 95 % confidence, with no prior estimate so the proportion is set to 0.5, you need 385 responses.
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Standard error of a proportion calculator
A yes share of 0.4 from 100 answers has a sampling variance of 0.0024, and its square root is the standard error: the typical wobble of that share between…
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One-Sample T-Test Calculator
Six measurements tested against a hypothesized mean of 11 give a positive t statistic, 5 degrees of freedom and a two-sided p-value just under five percent.
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Two-tailed critical value calculator
Turn a significance level into the two cutoffs of a two-sided z-test: at 0.05 the critical values are −1.96 and +1.96, with 0.025 in each tail and a 95%…
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Bartlett test calculator
Three groups with sample variances of 2.5, 5 and 10.2 give a p-value well above 0.05, so there is no clear evidence that their variances differ.
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Chi-square independence test calculator
A 2×2 table of 100 observations can give a chi-square of 4 on 1 degree of freedom and a p-value of about 0.0455, below the usual 0.05.
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Mann-Whitney U Test Calculator with P-Value
Compare two independent groups by rank instead of by mean: for 1, 3, 5, 7, 9 against 2, 4, 6, 8, 10 the smaller U is 10 and the two-sided p-value is…
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P-value from F statistic calculator
An F of 4 with 5 and 10 degrees of freedom has an upper-tail p-value just under 3%, so it is significant at the 5% level.
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Paired t-test calculator
Six subjects measured before and after give differences of 2, 4, −2, 4, 5 and 3: a positive mean change, 5 degrees of freedom and a two-sided p-value just under…
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Absolute risk reduction calculator
See how much a treatment lowered the risk in absolute terms: a control event rate of 0.20 and a treatment rate of 0.12 give an absolute risk reduction of 0.08…
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ANOVA from group summaries
Run a one-way ANOVA from group means, standard deviations and sizes alone: three groups of 4 with means 3, 5 and 7 and a deviation of 1 give an F of 16 and a…
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Log odds ratio calculator with standard error
Turn the four counts of a two-by-two table into a log odds ratio and its standard error: cells of 12, 5, 3 and 10 give an odds ratio of 8, whose natural log is…
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Omega squared calculator
With an effect sum of squares of 30, a total of 100, 2 effect degrees of freedom and a mean square error of 10, omega squared is 10 divided by 110: just under a…
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Relative risk calculator
40 events among 200 exposed people versus 20 among 400 unexposed give a relative risk of 4, so the outcome is four times as common with the exposure.
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Cohen's h calculator
Success rates of 0.70 and 0.30 give a Cohen's h above 0.80, a large effect. Enter two proportions to get the signed and absolute h, both transformed values and…
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Exponential moving average calculator
Five readings that start at 10 and climb by one each step, smoothed with a factor of 0.5, end at an EMA of 13.0625: recent values count more and older ones fade…
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Fisher ideal price index
A Fisher index of 1.05 means prices rose 5 % overall, measured as the geometric mean of Laspeyres and Paasche so that neither the old nor the new basket decides…
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Gini coefficient calculator
Turn a list of incomes or other non-negative values into one inequality score between 0 and 1: 0 means every value is equal, and the closer to 1, the more of…
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Rényi entropy calculator
Probabilities of 0.5 and 0.5 at order 2 give a Rényi entropy of 1 bit. Enter a list of probabilities or plain counts and an order α, and see the entropy, the…
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Simpson Dominance Index Calculator for Species Counts
Counts of 12, 8, 5 and 5 for four species add up to 30, and the index sums each species' squared share.
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Theil index calculator
Four incomes that total 100, with a mean of 25, give a Theil T index just above one tenth, while perfect equality would give zero.
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Arcsine in radians calculator
The arcsine of 1 is π/2 radians and that of −1 is −π/2. Enter any sine value from −1 to 1 and get its single principal angle in radians, ready for formulas…
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Cosine of angle in degrees calculator
The cosine of 180° is −1, and −60° has the same cosine as 60°. Enter any angle in degrees, positive, negative or above 360, and get its cosine between −1 and 1…
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Adjacent Side Calculator from Angle and Opposite Side
With a 45° angle and an opposite side of 10, the adjacent side is also 10. Enter any acute angle and the side across from it to get the missing leg of a right…
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Arccotangent in degrees calculator
The arccotangent of 1 is 45°, of 0 is 90° and of −1 is 135°. Enter any finite real number and get its single principal inverse cotangent angle in degrees…
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Arcsecant in degrees calculator
The arcsecant of 2 is 60° and that of −2 is 120°. Enter any number of 1 or more, or of −1 or less, and get in degrees the principal angle whose secant it is…
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Right triangle missing leg from area
Recover the side you are missing from the area alone: a right triangle with an area of 6 and one leg of 3 has a second leg of 4 and a hypotenuse of 5.
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Solve a right triangle from two legs
Solve the whole right triangle from its two legs: legs of 3 and 4 give a hypotenuse of 5, an area of 6 and a perimeter of 12, along with both acute angles.
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Secant of an Angle in Degrees Calculator
Type an angle in degrees and see its secant next to the cosine it comes from: 60° has a cosine of 0.5, so its secant is 2.
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Horizontal distance from elevation angle
An object 50 units tall seen at a 30° elevation stands 86.602540378444 units away horizontally, because the tangent of 30° is 0.57735026919.
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Law of sines missing side calculator
Get the one length your triangle is missing: with side a of 7, angle A of 40° and angle B of 60°, side b follows from b = a × sin B ÷ sin A, and the third angle…
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Solve an AAS triangle
Finish a triangle from two angles and a non-included side: angles of 50° and 60° leave 70° for the third, and the law of sines then gives both missing sides and…
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Sun elevation angle from shadow calculator
Measure an upright object and its shadow to learn how high the Sun is: when both are 2 metres, the Sun stands at 45° above the horizon.
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Tangent of angle in radians
Find the tangent of a radian angle without switching modes: π/4 gives exactly 1, with sine and cosine both 0.707106781187.
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Power reduction sine squared calculator
Lower the square on a sine in one step: for 30°, sin² becomes (1 − cos 60°) ÷ 2, and since cos 60° is 0.5 the value is 0.25.
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Product-to-sum cosine calculator
Turn a cosine product into a sum you can integrate or simplify: cos 60° × cos 30° becomes ½[cos 30° + cos 90°], and both forms give the same value.
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Pythagorean identity sin cos calculator
Recover the missing ratio with the right sign: a sine of 0.6 in quadrant II gives a cosine of −0.8, because cosine is negative there.
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Sine of difference of angles calculator
Find the sine of one angle minus another and see how it is built: for 75° and 30° the difference is 45°, and both products of the identity appear before they…
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Sine half-angle calculator
Find sin(θ/2) with the right sign every time: 90° halves to 45° and gives a positive result, while −90° halves to −45° and gives a negative one.
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Tangent of difference of angles calculator
Get the tangent of one angle minus another without expanding sines and cosines: 75° minus 30° leaves 45°, and tan(A − B) comes out as exactly 1.
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Tangent double-angle calculator
Double an angle's tangent without knowing the angle: a tangent of 0.5 gives a numerator of 1 and a denominator of 0.75, so tan(2θ) is 1 divided by 0.75.
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Triangle area from vertex coordinates calculator
Corners at (1, 1), (7, 1) and (4, 6) enclose an area of 15 square units. Enter the six coordinates of any three points that are not on one line and get the…
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General solution of sine equation
For sin θ equals 0.5, the principal angle is 30°, or 0.5235987756 radians, and every other solution follows from it by taking its supplement and adding whole…
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Gradians to radians conversion calculator
100 gradians, a right angle, convert to 1.570796326795 radians, which is π over 2. The rule is short: multiply by π and divide by 200, because 400 gradians make…
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